The only way to clarify these issues would be to experimentally introduce the oils in an effort to induce seizures whilst comparing this to a control group scrupulously avoiding the oils. However would this be ethical?
That would be one way, and I expect it would be ethical if you were clear with the participants about what you were doing and the doses were within the range of normal use of household products.
There are Material Data Safety Sheets that record known risks from products - so an easier way than doing an experiment is to look at the information that the MSDS's are based on. Typically there is information based on human exposures (acute and long term) and accidental and deliberate animal exposures. I found
an MSDS for camphor that reported these consequences of exposure:
Nausea,Headache, Shortness of breath. Irritation- all routes of exposure.The substance is irritating to the eyes , the skin and the respiratory tract . The substance may cause effects on the central nervous system , resulting in convulsions and respiratory depression. Exposure by ingestion may result in death;
It does look as though camphor and eucalyptus oil could cause seizures, although it probably takes high doses.
You could look at the incidence of seizures in workers who produce camphor and eucalyptus oil products.
Another way to bring some clarity would be to note how many patients came to the hospital with a first seizure and to record exposure to a range of possible causes, including flickering lights, sound and illness, with or without fever, as well as exposure to eucalyptus and camphor, and have a good look at the data. You would want to note the dose, as well as any other impacts on health. Perhaps that was done in this study, it just doesn't show in the abstract. (Edit - from the article linked in the second post, it does sound as if the study was more detailed than the abstract suggests.)
Another issue is that if a person did in fact have a seizure as a result of exposure to an essential oil, does that mean they have epilepsy? Probably, once they have recovered, they never have another seizure again. There's a big difference between causing a reactive seizure or episode of seizures, and triggering ongoing epilepsy.
Looking at the study abstract again, it just appears to be warning physicians that these substances can cause convulsions (as do many chemicals in big enough doses) and so the physicians should not immediately assume epilepsy if the patient has had some exposure.